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Correspondences of ribbon categories |
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| Authors: | Jü rg Frö hlich,Ingo Runkel |
| Affiliation: | a Institut für Theoretische Physik, ETH Zürich, CH-8093 Zürich, Switzerland b Institutionen för fysik, Karlstads Universitet, Universitetsgatan 5, S-65188 Karlstad, Sweden c Institut für Physik, Humboldt Universität Berlin, Newtonstraße 15, D-12489 Berlin, Germany d Fachbereich Mathematik, Schwerpunkt Algebra und Zahlentheorie, Universität Hamburg, Bundesstraße 55, D-20146 Hamburg, Germany |
| Abstract: | Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in ribbon categories. Finally, we establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory. |
| Keywords: | 18D10 81R10 81R50 81T40 |
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